1. Field of the Invention
The present invention relates to a corrected ball diameter calculating method and a form measuring instrument.
2. Description of the Related Art
Conventionally, as form measuring instruments that measure the dimensions and the profile of an workpiece, there have been known coordinate measuring machines, for example.
FIG. 10 is a diagram showing a conventional coordinate measuring machine 1.
The coordinate measuring machine 1 is equipped with a measuring machine body 2 and a personal computer (PC) 3 that processes measurement data acquired by the measuring machine body 2 to determine the dimensions and the profile of an workpiece W.
The measuring machine body 2 is equipped with a table 21, a gantry-type frame 22 that is disposed so as to be movable in an anteroposterior direction (the direction of the Y axis) on the table 21, a slider 23 that is disposed so as to be movable in a transverse direction (the direction of the X axis) along a horizontal beam 221 of the gantry-type frame 22, an ascending and descending shaft 24 that is disposed such that it may ascend and descend in the vertical direction (the direction of the Z axis) in the slider 23, and a probe 25 that is attached to the lower end of the ascending and descending shaft 24. A moving mechanism 26 that supports the probe 25 such that the probe 25 is movable in the triaxial direction is configured from the gantry-type frame 22, the slider 23 and the ascending and descending shaft 24. The probe 25 is equipped with a stylus 28 on whose distal a stylus tip 27 is disposed.
As methods by which the coordinate measuring machine 1 measures the workpiece W, point measurement and scanning measurement are commonly known.
In point measurement, the coordinate measuring machine 1 first causes the stylus tip 27 to sequentially touch measurement sites on the workpiece W while causing the probe 25 to move in the triaxial direction, whereby the coordinate measuring machine 1 acquires the coordinate values of the probe 25 in each touch point. Here, as shown in FIG. 11, the points of contact between the stylus tip 27 and the workpiece W exist in positions offset by an amount equal to the radius r of the stylus tip 27 from the center point P of the stylus tip 27 determined from the coordinate values of the probe 25. Consequently, the coordinate measuring machine 1 can determine the points of contact between the stylus tip 27 and the workpiece W from the coordinate values of the probe 25, so the coordinate measuring machine 1 can determine the dimensions and the profile of the workpiece W by using each of the coordinate values it has acquired to perform a predetermined operation.
In scanning measurement, the coordinate measuring machine 1 causes the probe 25 to move along the profile of the workpiece W in a state where the stylus tip 27 has been caused to touch the workpiece W and acquires the coordinate values of the probe 25 at a predetermined sampling pitch. Consequently, the coordinate measuring machine 1 can determine the dimensions and the profile of the workpiece W by using these coordinate values to perform a predetermined operation.
Incidentally, in measurement using the coordinate measuring machine 1, it is necessary to replace the stylus 28 depending on the measurement target, and the coordinate measuring machine 1 cannot automatically recognize the length of the stylus 28 and the diameter value of the stylus tip 27 disposed on the distal end of the stylus 28 when the stylus 28 has been attached. The length of the stylus 28 and the diameter value of the stylus tip 27 are values needed for determining the center point P of the stylus tip 27 from the coordinate values of the probe 25 and are values needed when determining the points of contact between the stylus tip 27 and the workpiece W from that center point P. For that reason, when the coordinate measuring machine 1 is used to measure an workpiece, it is necessary to perform, in advance, calibration that causes the coordinate measuring machine 1 to perform measurement of a master ball to cause the coordinate measuring machine 1 recognize the length of the stylus 28 and the diameter value of the stylus tip 27.
FIG. 12 is a diagram showing calibration.
In calibration, a diameter-calibrated value D of a master ball M is inputted to the coordinate measuring machine 1, and then the coordinate measuring machine 1 is caused to measure the master ball M, whereby the coordinate measuring machine 1 is caused to determine and recognize the length of the stylus 28 and the diameter value of the stylus tip 27. At this time, calculatory diameter values of the stylus tip 27 that are determined by measuring the master ball M ordinarily differ from diameter-calibrated values of the stylus tip 27 due to error that arises because of the affects of flexure of the stylus or the like when measuring the master ball M. Hereinafter, these calculatory diameter values of the stylus tip 27 will be called corrected ball diameters.
Incidentally, the magnitude of error that arises when measuring the master ball M differs depending on whether measurement of the master ball M is performed by static point measurement or dynamic scanning measurement. Consequently, corrected ball diameters that are determined by calibration differ depending on whether measurement of the master ball M has been performed by point measurement or scanning measurement. For that reason, when point measurement is performed by the coordinate measuring machine 1, it is necessary to use corrected ball diameters for point measurement that have been obtained by performing calibration by point measurement, and when scanning measurement is performed by the coordinate measuring machine 1, it is necessary to use corrected ball diameters for scanning measurement that have been obtained by performing calibration by scanning measurement.
In calibration resulting from point measurement, as shown in FIG. 12, the stylus tip 27 is caused to touch plural measurement sites on the master ball M to determine a measured diameter value Dp that is the diameter value of a circle passing through the neighborhood of the center points of the stylus tip 27 when the stylus tip 27 has touched each measurement site.
FIG. 13 is a diagram showing center points P1 of the stylus tip 27 that are recognized during point measurement.
At the time of this measurement, the center points of the stylus tip 27 end up being recognized as being in the positions of points P1 offset (e.g., slightly inward) by an amount equal to error G from the original positions P because of the affects of flexure of the stylus 28 or the like. For that reason, the measured diameter value Dp becomes a value including two parts of this error G. Thus, as shown in expression (1) below, by subtracting the diameter-calibrated value D of the master ball M from this measured diameter value Dp, a corrected ball diameter dp (a calculatory diameter value of the stylus tip 27) for point measurement including two parts of this error G can be determined.dp=Dp−D  (1)
FIG. 14 is a diagram showing calibration performed by scanning measurement.
In calibration resulting from scanning measurement, the circumference of the equator of the master ball M, the XZ in-plane semi-circumference of the northern hemisphere and the YZ in-plane semi-circumference of the northern hemisphere are profile-measured at a predetermined sampling pitch to determine a measured diameter value Ds in the same manner as mentioned before, and, as shown in expression (2) below, by subtracting the diameter-calibrated value D of the master ball M from the measured diameter value Ds, a corrected ball diameter ds for scanning measurement including two parts of the error G can be determined.d=Ds−D  (2)
Additionally, by dividing each of the corrected ball diameters dp and ds that have been determined in this manner by 2, the radius r1 (FIG. 13) of the stylus tip 27 including error G can be calculated depending on the measurement method. The center points of the stylus tip 27 are recognized by the coordinate measuring machine 1 as being in positions P1 including error G that arises depending on the measurement measure, so the coordinate measuring machine 1 can, by determining the positions offset by an amount equal to the radius r1 of the stylus tip 27 calculated depending on the measurement method (point measurement, scanning measurement) from the center points P1 of the stylus tip 27 that it recognizes, determine the points of contact between the stylus tip 27 and the workpiece W while controlling error G that arises depending on the measurement method and can analyze the profile and the like of the workpiece with high precision. In this manner, the coordinate measuring machine 1 can analyze the profile and the like of an workpiece with high precision by calculating beforehand the corrected ball diameters dp and ds including error G at the time of measurement and using these corrected ball diameters dp and ds to analyze the profile and the like of the workpiece.
Incidentally, in recent years there has been proposed a coordinate measuring machine that uses a rotary table to perform measurement while causing an workpiece to rotate (e.g., JP-A-2001-264048). The coordinate measuring machine described in JP-A-2001-264048 can efficiently measure an workpiece with a complex profile and can shorten the amount of analysis time of the profile and the like of the workpiece because the coordinate measuring machine can measure the workpiece with a total of four axes including three axes of a moving mechanism and one axis of the rotary table.
However, it has been found that when a rotary table is used in this manner to measure an workpiece and the corrected ball diameters are used to analyze the profile and the like of the workpiece, error ends up arising in the analysis result even though the error is slight. Moreover, it has been found that this error is affected by the height position of the workpiece that is measured. It is thought that when an workpiece is measured while the workpiece is caused to rotate, error resulting from measuring the workpiece while causing the workpiece to rotate and error corresponding to the height position that is measured arises because of runout of the rotary table, whirl of the workpiece and flexure of the stylus or the like, and error ends up arising in the analysis result because of these measurement errors.
That is, it is thought that because error that arises by measuring an workpiece while causing the workpiece to rotate and error that arises depending on the height position that is measured are not included in the conventional corrected ball diameters that are calculated by measuring the master ball M in a stationary state, when the conventional corrected ball diameters are used to analyze the profile and the like of the workpiece when the workpiece has been measured while the workpiece has been caused to rotate, analysis precision ends up dropping in correspondence to these errors not being included in the corrected ball diameters.